An analysis of the problem of wave-front reconstruction from Shack-Hartmann measurements is presented. The wave-front aberration is assumed to result from passage of the wave front through Kolmogorov turbulence. Limitations of using Zernike polynomials as an orthogonal basis for wave-front reconstruction are highlighted, and the advantage of using the Karhunen-Loeve functions for computing the higher-order modes of the wave front is shown.